Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Unraveling materials' Berry curvature and Chern numbers from real-time evolution of Bloch states

19.02.2019

Researchers from the Theory Department of the Max Planck Institute for the Structure and Dynamics of Matter (MPSD) at the Center for Free-Electron Laser Science (CFEL) in Hamburg and UNIST (Ulsan National Institute of Science and Technology) in Korea used a state-of-the-art quantum dynamical method to calculate the quantum of spin or charge Hall conductivity, by which they successfully classified the intrinsic topological natures of materials. Their work has been published in PNAS.

Einstein is commonly quoted as saying: "The most incomprehensible thing about the world is that it is comprehensible.  The fact that it is comprehensible is a miracle.”


The exact opposite transversal flow of spin-up and spin-down electrons, leading to zero charge Hall conductivity but with a finite quantized spin Hall conductivity.

Dongbin Shin

This statement is derived from an article he wrote in 1936 for the Journal of the Franklin Institute. From a physicist’s perspective, such a ‘miraculous comprehension’ most likely indicates that the observed phenomena are very well interpreted by the natural laws, expressed as mathematical equations.

On the other hand, the objectivity and indispensability of mathematical knowledge have been debated ever since Plato and Aristotle. Similarly, questions regarding the role of mathematics in the study of physical phenomena have been raised in recent solid state physics, particularly on the topological notion of insulators.

Thouless et. al. proposed in 1982¹ that the Hall conductivity of an insulator is to be quantized as indexed by a mathematically-devised integer, reflecting the topological structure of the quantum mechanical nature.

Since then, Michael Berry (1984)² has identified that such a mathematical number should be related to the phase structure of the quantum mechanical wave-function. According to Haldane (1988)³ and Kane and Mele (2005)⁴, real materials can be geared by spin-orbit coupling to possess such a non-trivial topological number. This has resulted in a wealth of studies to explore topologically non-trivial materials, particularly for the systems preserving time-reversal symmetry.

In this very mathematical characterization of physical systems, a great doubt is cast over the realness of the mathematically devised number or whether the topological constant can be measured experimentally. Instead of directly contemplating on this issue, the team has developed a computation method that can accurately calculate the Hall conductivity of insulators.

The scientists found that the entire classification of these materials can be achieved by their conductivity itself instead of the mathematically devised topological number. By calculating the time-dependent quantum mechanical equation, they were able to numerically quantify the electrons’ velocity, which was formulated by Michael Berry (1984). The summation of the electrons’ velocity is to be quantized and the detailed intrinsic quantum mechanical structure can be labelled by those quantum numbers.

In short, the team proposes to use physical quantity, less contaminated by mathematical notion, to characterize the materials’ properties, which provide a more direct link to experimental measurements.

REFERENCES

1 D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Physics Review Letters 49, 405 (1982)

2 M. V. Berry, Quantal Phase-Factors Accompanying Adiabatic Changes, Proc. R. Soc. Lon. Ser-A 392, 45 (1984).

3 F. D. M. Haldane, Model for a Quantum Hall-Effect without Landau-Levels-Condensed-Matter Realization of the Parity Anomaly, Physical Review Letters 61, 2015 (1988)

4 C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Physical Review Letters 95, 22 (2005)​

Wissenschaftliche Ansprechpartner:

Noejung Park (corresponding author): noejung@unist.ac.kr
Jenny Witt, PR officer, MPSD: jenny.witt@mpsd.mpg.de / +49 (0)40 8998 6593

Originalpublikation:

https://www.pnas.org/content/early/2019/02/13/1816904116

Jenny Witt | Max-Planck-Institut für Struktur und Dynamik der Materie
Further information:
http://www.mpsd.mpg.de

More articles from Physics and Astronomy:

nachricht Researchers put a new spin on molecular oxygen
17.07.2019 | Osaka University

nachricht Harvesting energy from the human knee
17.07.2019 | American Institute of Physics

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Megakaryocytes act as „bouncers“ restraining cell migration in the bone marrow

Scientists at the University Würzburg and University Hospital of Würzburg found that megakaryocytes act as “bouncers” and thus modulate bone marrow niche properties and cell migration dynamics. The study was published in July in the Journal “Haematologica”.

Hematopoiesis is the process of forming blood cells, which occurs predominantly in the bone marrow. The bone marrow produces all types of blood cells: red...

Im Focus: Artificial neural network resolves puzzles from condensed matter physics: Which is the perfect quantum theory?

For some phenomena in quantum many-body physics several competing theories exist. But which of them describes a quantum phenomenon best? A team of researchers from the Technical University of Munich (TUM) and Harvard University in the United States has now successfully deployed artificial neural networks for image analysis of quantum systems.

Is that a dog or a cat? Such a classification is a prime example of machine learning: artificial neural networks can be trained to analyze images by looking...

Im Focus: Extremely hard yet metallically conductive: Bayreuth researchers develop novel material with high-tech prospects

An international research group led by scientists from the University of Bayreuth has produced a previously unknown material: Rhenium nitride pernitride. Thanks to combining properties that were previously considered incompatible, it looks set to become highly attractive for technological applications. Indeed, it is a super-hard metallic conductor that can withstand extremely high pressures like a diamond. A process now developed in Bayreuth opens up the possibility of producing rhenium nitride pernitride and other technologically interesting materials in sufficiently large quantity for their properties characterisation. The new findings are presented in "Nature Communications".

The possibility of finding a compound that was metallically conductive, super-hard, and ultra-incompressible was long considered unlikely in science. It was...

Im Focus: Modelling leads to the optimum size for platinum fuel cell catalysts: Activity of fuel cell catalysts doubled

An interdisciplinary research team at the Technical University of Munich (TUM) has built platinum nanoparticles for catalysis in fuel cells: The new size-optimized catalysts are twice as good as the best process commercially available today.

Fuel cells may well replace batteries as the power source for electric cars. They consume hydrogen, a gas which could be produced for example using surplus...

Im Focus: The secret of mushroom colors

Mushrooms: Darker fruiting bodies in cold climates

The fly agaric with its red hat is perhaps the most evocative of the diverse and variously colored mushroom species. Hitherto, the purpose of these colors was...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

2nd International Conference on UV LED Technologies & Applications – ICULTA 2020 | Call for Abstracts

24.06.2019 | Event News

SEMANTiCS 2019 brings together industry leaders and data scientists in Karlsruhe

29.04.2019 | Event News

Revered mathematicians and computer scientists converge with 200 young researchers in Heidelberg!

17.04.2019 | Event News

 
Latest News

Tracking down climate change with radar eyes

17.07.2019 | Earth Sciences

Researchers build transistor-like gate for quantum information processing -- with qudits

17.07.2019 | Information Technology

A new material for the battery of the future, made in UCLouvain

17.07.2019 | Materials Sciences

VideoLinks
Science & Research
Overview of more VideoLinks >>>